Unitarity, clock dependence and quantum recollapse in quantum cosmology
Unitarity, clock dependence and quantum recollapse in quantum cosmology
复制标题
量子宇宙学中的幺正性、时钟依赖性和量子塌缩
DOI：
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发表时间：
2021
影响因子：
3.5
通讯作者：
Luc'ia Men'endez
中科院分区：
文献类型：
--
作者：
Steffen Gielen;Luc'ia Men'endez
我们继续分析量子宇宙学模型，该模型描述了一个充满(自由)无质量标量场和任意理想流体的平坦Friedmann-Lemaütre-Robertson-Walker宇宙。对于标量和流体中的正能量密度，每个经典解都有一个奇点，并扩展到无限体积。在量化时，我们用关系术语来看待宇宙动力学，使用一个自由度作为其他自由度的时钟。这个钟的三个自然候选者是体积、理想流体的时间变量共轭和标量场。我们以前已经证明，在‘流体’时间中要求么正演化导致在奇点和一般奇点分辨下的边界条件，而在体积时间中半经典态遵循经典的奇异轨迹。在这里，我们分析了使用标量场作为时钟的第三种选择，发现与前面的情况有更大的不同：由一元性引起的边界条件现在是无穷大的。这一理论不是奇点分解，而是大体积宇宙的量子重陷，正如Pawłowski和Ashtekar在类似的背景下所展示的那样。我们从解析和数值上说明了该理论的性质，表明不同的量子理论是否偏离经典行为的方式直接源于对不同时钟的统一性的要求。我们认为，使用狄拉克量化并不能解决这个问题。我们的结果进一步说明了量子引力中的时间问题。
We continue our analysis of a quantum cosmology model describing a flat Friedmann–Lemaître–Robertson–Walker Universe filled with a (free) massless scalar field and an arbitrary perfect fluid. For positive energy density in the scalar and fluid, each classical solution has a singularity and expands to infinite volume. When quantising we view the cosmological dynamics in relational terms, using one degree of freedom as a clock for the others. Three natural candidates for this clock are the volume, a time variable conjugate to the perfect fluid, and the scalar field. We have previously shown that requiring unitary evolution in the ‘fluid’ time leads to a boundary condition at the singularity and generic singularity resolution, while in the volume time semiclassical states follow the classical singular trajectories. Here we analyse the third option of using the scalar field as a clock, finding further dramatic differences to the previous cases: the boundary condition arising from unitarity is now at infinity. Rather than singularity resolution, this theory features a quantum recollapse of the Universe at large volume, as was shown in a similar context by Pawłowski and Ashtekar. We illustrate the properties of the theory analytically and numerically, showing that the ways in which the different quantum theories do or do not depart from classical behaviour directly arise from demanding unitarity with respect to different clocks. We argue that using a Dirac quantisation would not resolve the issue. Our results further illustrate the problem of time in quantum gravity.
影响因子：
2.9
作者：
M. Bojowald
通讯作者：
M. Bojowald
奇点分辨率取决于时钟
影响因子：
3.5
作者：
Gielen S
通讯作者：
Gielen S